1. Field of the Disclosure
The disclosure relates generally to antennas and, more particularly, to the fabrication of electrically small antennas on three-dimensionally contoured substrates.
2. Brief Description of Related Technology
With the expansion of the wireless mobile market, interest in electrically small antennas has surged in recent years. See, for example, Best, “The radiation properties of electrically small folded spherical helix antennas,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 4, pp. 953-960 (April 2004), and Erentok et al., “Metamaterial-Inspired Efficient Electrically Small Antennas,” IEEE Transactions on Antennas and Propagation, vol. 56, no. 3, pp. 691-707 (March 2008). In many cases, the size of the antenna limits the minimum achievable size of the wireless device itself.
A common method of making an efficient electrically small antenna is to use a small dipole antenna in combination with a matching circuit. This approach generally leads to very narrow bandwidths and relatively low efficiencies. Other methods include packing resonant, magnetically coupled antenna elements into a small volume, and using space filling curve antennas and fractal curve antennas. Please see, for example, Stuart et al., “Small Spherical Antennas Using Arrays of Electromagnetically Coupled Planar Elements,” IEEE Antennas and Wireless Propagation Letters, vol. 6, no. 1, pp. 7-10 (July 2007), and Best, “On the performance properties of the Koch fractal and other bent wire monopoles,” IEEE Transactions on Antennas and Propagation, vol. 51, no. 6, pp. 1292-1300 (June 2003).
Antennas are considered to be electrically small when their maximum radial dimension (ka) is less than 0.5 radians, where k=2π/λ is the free space wave number, and a is the radius of the minimum sphere which circumscribes the antenna. Maximizing an antenna's bandwidth is equivalent to minimizing its quality factor (Q). It has been shown that the minimum achievable Q factor for electrically small antennas is Qchu=1/(ka)+1/(ka)3. Please see Chu, “Physical limitations of omni-directional antennas,” Journal of Applied Physics, vol. 19, pp. 1163-1175 (December 1948), and McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Transactions on Antennas and Propagation, vol. 44, no. 5, pp. 672-676 (May 1996). The ratio of an antenna's Q to Qchu is a common figure of merit for characterizing small antennas.
Spherical helix antennas have been shown to closely approach the Chu limit. Spiraled metallic wires in the shape of a hemisphere have been formed by manually bending the metallic wire around a sphere. Unfortunately, the manual nature of that step has made fabrication of these antennas time consuming, inaccurate and expensive.